[math-fun] Excellent Wikipedia hypocycloid animation

https://upload.wikimedia.org/wikipedia/commons/d/da/Rolling_Hypocycloids.gif This is the decacuspid (n=10) case. What happens when n➝∞? Why do all the curves coincide only at 3 o'clock and 9 o'clock? Why isn't https://en.wikipedia.org/wiki/Epicycloid nearly as complete as https://en.wikipedia.org/wiki/Hypocycloid? Telling us, e.g., the area of Julian's <http://gosper.org/tripenta.gif> trisectrix (astroid) but not the pentasectrix (quadricuspid epicycloid). Kids: I somehow missed (or completely forgot) the cool integral for the area of the curve enclosed by {x(t),y(t)}: ½∲(x dy - y dx). Supposing a unit radius, what's the area of one of those four "cabochons"? —rwg